The first and more manifest way is the argument from motion. It is
certain, and evident to our senses, that in the world some things are in
motion. Now whatever is in motion is put in motion by another, for
nothing can be in motion except it is in potentiality to that towards
which it is in motion; whereas a thing moves inasmuch as it is in act.
For motion is nothing else than the reduction of something from
potentiality to actuality. But nothing can be reduced from potentiality
to actuality, except by something in a state of actuality. Thus that
which is actually hot, as fire, makes wood, which is potentially hot, to
be actually hot, and thereby moves and changes it. Now it is not possible
that the same thing should be at once in actuality and potentiality in
the same respect, but only in different respects. For what is actually
hot cannot simultaneously be potentially hot; but it is simultaneously
potentially cold. It is therefore impossible that in the same respect and
in the same way a thing should be both mover and moved, i.e. that it
should move itself. Therefore, whatever is in motion must be put in
motion by another. If that by which it is put in motion be itself put in
motion, then this also must needs be put in motion by another, and that
by another again. But this cannot go on to infinity, because then there
would be no first mover, and, consequently, no other mover; seeing that
subsequent movers move only inasmuch as they are put in motion by the
first mover; as the staff moves only because it is put in motion by the
hand. Therefore it is necessary to arrive at a first mover, put in motion
by no other; and this everyone understands to be God.

Introduction

This argument is a variation of the cosmological argument, one of the most
important philosophical arguments for the existence of God. I am writing
this post in response to a criticism that was brought to my attention on
the Thomas Aquinas
facebook group that claimed that this argument was effectively
disproved by modern physics.

I'll get to the objections in a moment, but first of all I want to
outline the main steps of Aquinas' argument.

Some things are in motion.

Everything in motion must have been put into motion by something else.

This chain of movers and moved is a hierarchical rather than an
accidental series.

Every hierarchical series must have a primary member; in this case
something which moves others but is not moved itself.

Therefore there must be at least one unmoved mover.

Therefore there must be at least one unmovable mover.

This being is God.

Many critics pounce on the last two steps, and ask how we get to God from
an unmoved mover. In part, it is down to definition. The classical
definition of God is simply a being of pure actuality, that is to say
something devoid of potentiality, and therefore incapable of change.
The second part is that God is act, i.e. interacts with the world, so
moves others.
So, by definition, God is an
unmovable mover. To anyone who complains that the definition of God must
include attributes such as omnipotence, omniscience and so on, that's
your choice. We can quibble over definitions if you like.
It's no obstacle to the theist, because
Aquinas (and just
about everyone else who has wielded the cosmological argument in any more
than a brief article such as this) has shown that such attributes follow
directly from the definition. I devote chapter 13 of my own book
here to the task, and others have
done it in more detail and rigour than I did. An important part of that
argument is to overcome the other obvious objection to this part of the
argument, namely why must there be only one unmoveable mover (how do we get from
at least one at the end of the cosmological argument to a singular God).

But that's not the topic I want to discuss here. All the cosmological
argument does is show that there is at least one unmovable mover; to
go beyond that requires further argumentation. So let us keep that as our
immediate goal. I am here more concerned with
the first few steps of the argument. And before I get onto them, I need to
unpack them and explain them to those not familiar with the philosophy.

I'll start with the distinction between a hierarchical series compared to
an accidental series. Each of these represent chains, in the simplest and
easiest to visualise form, where one member is
linked to another which is linked to another and so on. The only direct
interaction between members of the chain is with their neighbours
(in the language of physics, the direct interactions are local). But what
about indirect influence? So let us say that A is a member of a
chain and Z is another member, and they are not neighbours.
Does A influence the state of Z, with everything between
them acting as instruments? In the specific example of the series of
movers, can
the motion of Z ultimately be attributed to the power of A
to move? There are three possible answers to this question: yes,
no, and
in part. A hierarchical series is one where the answer is either
yes or in part.

An analogy that I like to use is that of a series of train carriages. Suppose
that the carriages are moving. The carriage we are in is pulled by the
carriage next to it. That carriage is pulled by the carriage next to that.
And so on. Eventually, you get to an engine, that is to say something
that is capable of pushing the carriage next to it without being pushed
itself. Now, if the carriages are in motion, then there must be an engine.
So if there is one carriage in motion, it must be coupled to an engine.
If there are two carriages, at least one of them must be coupled to an
engine. If there are N carriages, then at least one of them must
be coupled to an engine. And this remains true even when we take N
to infinity. The engine is what I have called the primary mover.
(This translation of Aquinas calls it
the first mover, but that translation is slightly misleading to the
modern ear, since the
first merely implies the end of the chain, and not this special property
of being able to move without being moved itself. The chain could be infinite,
but it would still need a primary mover.) So this is a
hierarchical series.

One of the examples that Aristotle used to illustrate
the series was a hand moving a stick moving a stone, which perhaps moves
another stone and that another stone and so on. The point is that the
stones themselves cannot initiate the motion, no matter how many stones
you have. There must be a hand at the start of the series. Aquinas refers
to this analogy in the first. The students who first read his work,
who, at this stage of their education would have been experts on all the
Socratic philosophers including Aristotle, would have
immediately picked up on the reference and understood his meaning. In our
degenerate days with a different educational emphasis, the concept needs
explaining. Which is why I have just explained it.

An accidental series would be like a group of train carriages coupled
together without an engine. Here one could (in principle, if not in
practice) have an infinite number of carriages without an engine.
Perhaps the carriages are stationary. Perhaps they each have their own
in-built engines. In either case, there doesn't need to be a primary
mover pushing the system along.

So what distinguishes a hierarchical series from an accidental one?
There are various possibilities.

In a hierarchical series, there is a definite direction of causality.
Something moves something else which moves something else and so on.

In a hierarchical series, there is an asymmetry between the two different
neighbours of a chain. One of them pulls, the other is pulled.

In a hierarchical series, there is an indirect dependence between
non-neighbouring members of the chain. A directly pushes B,
but can also be said to be indirectly pushing Z.

In a hierarchical series, the interactions are in some way simultaneous
with each other. The hand pushes the stick while the stick is pushing
the stone. (A causal sequence isn't necessarily a temporal sequence.
This point is important.)

Non-primary members of a hierarchical series are incapable of moving
themselves (to use
the specific example of the series referred to in the first way). In
other words they by themselves do not contain an explanation of their
change.

If the series is static (things do not change their
state) then the series is accidental.

Hopefully, it is clear from my examples that a hierarchical series needs
to have at least one primary member (while that is not true for an
accidental series).

Every cosmological argument sets up a sequence of some sort, claims that
that sequence cannot continue indefinitely, concludes that the sequence
must have a first member, and identifies that first member with God.
This business with the hierarchical series is how Aquinas (and Aristotle
before him) argued the sequence could not continue indefinitely. Now, I
should hasten to add that this is not the only argument one can use to
justify that step. But it is the argument used in the first way, so it is
what I will focus on here.

The second concept I need to discuss is that of motion. This word is
confusing, because Aristotle and Aquinas meant something very different
by the word than we do today. Our understanding of the word is a legacy of
the early mechanists and the enlightenment, who assumed that the only
type of motion (in the sense that Aristotle meant the word) of physical
relevance was local or locomotion, i.e. movement from place to place.
We have inherited that, and when we think of motion, we think of
locomotion. But when we come to the first way, we then get confused.
I will put the source of the confusion clearly: locomotion is not motion
in the sense used by Aristotle and Aquinas.

That statement would come as
a big surprise to the Aristotelian philosophers. But that's because their
physics was wrong. They had a version of Newton's second law, which was
that force is proportional to velocity. Newton, of course, proposed
that force is proportional to mass times acceleration (equal to, if one
chooses convenient unity to measure things in). The Aristotelian physicists
(not, I think Aristotle himself -- I am being anachronistic in my
language; but I am talking about his late medieval successors) would define force
as something which induces a motion. So in Aristotle's physics,
motion can be equated to velocity. Newtonian physics removes that link.
Something has got to change somewhere. We either have to no longer
equate motion with velocity, or no longer define force as something that
induces a motion. The early modern philosophers chose the second option.
I think that was the wrong decision.
In doing so, they undermined the deeper classical concept of motion,
and made it impossible for their followers (which includes
people of our generation, since English and other modern languages
developed to follow their lead) to understand arguments such as
the first way.

Of course, Aristotle's physics is not as bad as it might seem to someone
who has had too many classes on classical mechanics. Force is proportional
to velocity is how things seem to work in the world around us. That's
what induction from a basic experiment will tell you (and, presumably
why Aristotle came up with the idea that I expressed in that formula).
This is because of friction. Friction is a force acting on a body
travelling through a gas or a liquid that is, to a good approximation,
proportional to the velocity of that body. To keep the body moving at
constant velocity, one needs to apply an equal force in the opposite
direction. If one only measures the force one directly applies, and
neglects the friction, it will
indeed appear as though force is proportional to the terminal velocity
of the being (with the
constant of proportionality dependent on the density of the medium,
the mass of the body, and also its coefficient of friction determined by
its shape and texture, among other things).

But, of course, we live in a post-Newtonian world, and know that force is
instead associated with acceleration. (Indeed, we live in a post-quantum
world, and know that even this is too simple.)
So now it is a matter of translating
Aristotle's terminology into that reality. Which means delving into what
the concept of motion really meant to the Aristotelian philosopher.

The concept, as Aquinas stated in the first way, is derived from the
concept of actuality and potentiality. In addition to actual existence and
non-existence, something can exist potentially. That is that it exists
within the being as a possible state it could change into. Every being
could exist in a multitude of stable or meta-stable states. One of those
states is actualised at any given time. Motion is when a being stops
being in one state and moves to another. One of the potential states is
actualised, and what was the actual state ceases to be actual and becomes
potential.

Each meta-stable state has a natural motion towards a stable state. In
Aristotle's physics, this stable state is to be at rest in relation to the
centre of the universe (which is the centre of the earth). Now, obviously
this is wrong. Newtonian physics, on the other hand, posits that bodies
have a natural tendency to continue at the same velocity or momentum
(mass times velocity). The state is defined by location and momentum.
Thus a body will naturally maintain a constant momentum, and change its
location at a constant rate.

In addition to this natural motion, we have artificial motion. This is
when something is forcibly moved from one state to another by an external
agent, against its natural tendency. In Aristotle's terms, an example
would be when we lift a stone off the floor. In Newtonian physics, this
might be when we divert the course of an Imperial Star Destroyer by
ramming our corvette into it.

The first way was originally conceived in a world-view that accepted
Aristotelian physics. Indeed, it was originally conceived by Aristotle
himself. Defenders of the first way, however, state that the
philosophical basis stands apart from that physics, and can be
adapted to modern physics. In that case, it should be possible to
translate the first way into a language more amenable to modern science.
In particular, we are going to have to adapt what is meant by the concepts
of motion and thing to remain as true as possible to the
spirit of what Aquinas meant by those terms in the light of subsequent
developments in physics.

There are two main questions which need answering:

Is it true that whatever is in motion is put in motion by another.

Is it true that the chain on movers and moved is a
hierarchical rather than accidental series?

The first way and Newtonian Physics

The objection.

I was asked to write this post in answer to a comment by an internet user,
who claimed to have found a way to refute the first way. (Actually, I
wasn't asked to write this post, but only to comment on the objection, but
this is my way of commenting). The objection is the following:

The First Way also hinges on the assertion of the impossibility of an
infinite regress.

The erroneous world-view of Aquinas is what leads him to a hierarchical
regress analysis in his first three ways.

If an object in uniform linear motion required "another" to act upon it
to sustain its motion then a hierarchical regress would be called for.

If an object needed a cause to persist in existence then a hierarchical
regress would be called for. But as someone pointed out "Whoa, where
did that come from?"

An object in uniform linear motion persists in motion because there is
no change in its kinetic energy to do so, and no change means no
changer is necessary to account for observed uniform linear motion.

An existent object persists in existence because there is no change in
its mass/energy to do so, and no change means no changer is necessary
to account for observed existential inertia.

If an object in uniform linear motion had to be externally acted upon
to maintain its uniform linear motion the First Way would make sense
and be a very powerful argument for a hierarchical first mover in the
present moment.

In that case the uniform linear motion of X1 would
require an X2 to act
upon it. Then X2 would require an
X3 to act upon it, and so forth,
calling for a first mover that acts upon Xn
without itself being acted
upon.

However, it is manifest and evident to the senses that uniform linear
motion persists without any external actor.

To act upon an object in order to move it is to apply a force to it.
The application of a force to an object that imparts motion transfers
kinetic energy to that object and accelerates that object approximately
by F=ma.

An object in uniform linear motion does not change in its mass/energy.
Since it does not change in its mass/energy there is no necessity of an
external actor upon that object, because no change calls for no changer.

Thus, the First Way is false as an argument for the necessity of a
first mover to account for observed uniform linear motion.

Thus, I have utterly destroyed the First Way. I have utterly destroyed
the Second Way. As arguments for the necessity of a hierarchical first
mover both fail under my clear and unrefuted arguments.

This objection defines motion as linear motion in a straight line and at
constant velocity. It then states that this motion continues interrupted.
Changes in this motion are thus disjoint. It is not necessary that the
thing moving the object is at that time being pushed by something else, as
in the example of the stick pushed by the hand and pushing the stone.
Indeed, it is not necessary that there is any outside mover at all.
If there is any series of movers, it is disjointed and thus not
hierarchical. Therefore there is not the sort of hierarchical series of
movers needed by the first way. Therefore the first way is false.

Now I am here discussing Newtonian physics (as in the physics of Newton's
day), where forces are transferred
by physical contact. I will discuss electromagnetic and gravitational
forces in later sections. So acceleration is caused when something pushes
against it. Now that thing doing the pushing must also be accelerating.
Either it is a rigid body, or perhaps a body that was compressed and is
now expanding back to its original state -- but even there, the part that
is expanding is being pushed by the released energy, which is itself the
result of something else changing, and so on (although we soon get down to
the molecular and atomic level and thus quantum physics, which I am not
discussing at this point). Now this is precisely the sort of series that
Aquinas and Aristotle were referring to in the first way.

Thus as long as as we define motion to be acceleration rather than
loco-motion, which is truer to Aristotle's definition of motion as being
from one meta-stable state to another, then we run straight into the
requirements of the first way. Newton's first law guarantees that
everything that is moved (i.e. accelerated) is moved by something else,
and the series we get is completely analogous to Aquinas' example.

The primary error of the objection was to assume that because motion and
locomotion can be equated in Aristotle's physics, they should also be
equated in Newtonian physics. That assumption was not justified, and I
have argued that it is, in fact, false.

Further objection

In Newtonian physics, a state is defined by two, and only two,
parameters: location and momentum. However, the argument above defines
states in terms of a single parameter, momentum. Therefore locomotion
is still a change from one state to another, and thus counts as a type
of motion. The first way can't be used to describe this change of state.

Response.

Aristotle, of course, knew nothing of the importance of momentum. He only
described location and linear velocity. Thus states (for Aristotle) were
determined by location -- not only by location (he considered other types
of change, such as change in temperature), but not including velocity.
Aristotle also had this distinction between natural and artificial motion.
But the two concepts in Aristotle's thought are somewhat confused. They
act on the same parameter space. Newtonian mechanics places a clear
distinction between them. Natural motion affects the location of a
particle. Artificial motion results in a change in its momentum.

The existence of natural motion doesn't invalidate the first way.
If it did, one wouldn't need to appeal to Newtonian physics.
Both Aristotle and Aquinas acknowledged it. The first way only
requires that artificial motion forms a hierarchical series. That there is
also natural motion does not preclude that the sort of motion needed by
the first way also exists. Indeed, it could be thought that Newtonian
physics in this respect strengthens Aquinas' hand by making the
distinction between the two types of motion clear.

This objection is fully resolved in quantum physics, because there the
states are solely described by momentum, as discussed below. We are left
with a system entirely analogous to Aristotle's physics.

Further objection

Natural motion in Aristotle's thought is characterised by motion towards
some end. Inertial motion continues indefinitely. Therefore the two can't
be equated.

Response

As already seen with the concept of motion, when adapting Aristotle to
modern science, we have to divorce some of his categories with the
physical consequences that he applied them to, and reattach them to
different concepts in physics. In Aristotle's physics, natural motion
has a tendency towards an end. For example, the natural motion of a brick
(which is predominately made of the element of earth)
is towards the centre of the universe. In Newtonian physics, we keep the
concept of natural motion, but change its end.

But doesn't the concept of an end indicate a degree of finality? A body
undergoing linear motion in Newton's physics continues to infinity, and
infinity does not have an end. But Aristotle was comfortable with the idea
that natural motion could continue forever. Quintessence, the material
which (in Aristotle's view) the stars and planets were made of, had a
natural motion of circling the centre of the universe. It would
continue indefinitely, rather than reaching some final destination. Again,
fire had a natural motion away from the centre of the universe. No end
there. So it is not true that natural motion necessarily implies an end.

Nor is it true that there are no ends in classical physics.
It is not true for complex systems of particles; thermodynamics states
that these tend towards a state of statistical equilibrium or maximum
entropy. General Relativity changes the concept of inertia. It is no
longer that things naturally travel at constant velocity unless an
external force is applied, but that things naturally travel along
geodesics of the metric unless an external force is applied. Geodesics
need not be straight lines with constant velocity. That is only true in
flat geometries such as the Euclidean geometry that underlies Newtonian
physics, or the hyperbolic geometry that underlies special relativity.
Geodesics in the more complex geometries of general relativity can be
circles, or lines heading into a black hole. When something falls under
the force of gravity, it is undergoing natural motion along a geodesic. It
seems that Aristotle's and Einstein's theories of gravity are far closer
than many would give them credit for. The difference, of course, is that
(were the earth not there, and there was no friction) Aristotle's falling
body would come to a rest at the centre of the earth, while Einstein's
will oscillate around that centre. But both are following natural motion,
as Aristotle defined it.

The first way and Maxwell-Faraday Physics

Objection

My internet friend didn't reach this far, but if we go a couple of
centuries beyond Newton, we have a more serious difficulty for the first
way than the principle of inertia.

The argument above assumed that acceleration was only caused by contact.
However, we know that that is not true. The electromagnetic force is a
clear example. Here we have force at a distance. Each charged particle
generates by itself an electric force which draws other charged particles
into it or away from it. Thus a charged particle can move others based on
its own inherent power.

This means that while there might be a series of movers and moved required
by the first way, it is not the hierarchical series needed by Aquinas in
which most of the members are inert intermediaries between God and the
object being moved.

The basic problem are these. Firstly, the force between charged particles
is mutual and mechanistic. There is no asymmetry; no direction of
causality. Indeed, it is not clear that the concept of causality is
useful here. Secondly, the particles generate the force themselves.
Every charged particle generates an electric force. It does not need to
be moved itself in order to move others. It just does it automatically.

Response

As discussed, there are two principles in the first way which need
defending, with everything else basically following from these or the
definitions, or being self-evident. The first is the principle that every
motion needs a mover. I have argued that this remains true in classical
physics; indeed, it is demanded by Newton's first law once we have defined
our terms correctly. The second notion is that the sequence of movers and
moved is hierarchical rather than accidental. While a lot of responses to
the first way concentrate on the first premise, it is this second one
which in my view is the harder of the two to justify. This objection
targets the second premise. It acknowledges the existence of motion
(correctly defined as acceleration); acknowledges the sequence of movers
and moved, but denies that that chain is a hierarchical series and instead
asserts that it is an accidental series.

In my answer here, I will be using Maxwell and Faraday's conception of
electromagnetism, and bring in elements from special relativity.

Certainly, Aquinas' example of the stick pushing the stone no longer seems
relevant in the context of the electromagnetic force. It is not the
case of one thing being moved itself and on account of that motion pushing
something else. So is there some
other way of determining whether the series is hierarchical or accidental?

First of all, we need to be more specific in describing the
electromagnetic force. Maxwell and Faraday established that the early
mechanists got something wrong. They believed that the only things that
influenced physics were corpuscles, location and motion. Corpuscles are
discrete and localised. Localised means that they only exist at one point
in space. Discrete means that the number of particles has to be an
integer. It is not a generic real number. Faraday and Maxwell
introduced the second concept of fields. Classical fields are continuous
and de-localised. De-localised means that that they are spread across all
space. Continuous means that the intensity of the field (the closest
analogy to particle number) can take any real value.

Note that the physical field is not the electromagnetic force,
usually denoted by E or B in the physics
textbooks, but the electromagnetic potential. The potential energy of
the electric force is usually denoted by φ, and the magnetic
potential as A. The relationship is that the force is the
variation of the potential field in space
(E = ∇φ;
B = ∇× A).

The electromagnetic force is an interaction between corpuscles and fields.
Variations in field strength generate forces on corpuscles. The fields
themselves, in the absence of corpuscles have a natural motion
described by Maxwell's equations. The motion of particles induces changes
in the fields. Each interaction is localised, so it comes through contact.
So there is no action at a distance. So one could say that the particles
are pushed by the fields, which in turn push the particles.

Now we have to think about how this translates into Aristotelian
terminology. It seems clear to me that we have to treat both fields and
corpuscles as different types of matter. Fields move further away from
Aristotle's vision of matter; but that vision is a physical application of
the underlying philosophical principle, and we are trying to ditch the
original physical application to preserve the philosophy as much as we
can. Fields exist (this can be demonstrated experimentally), they are not
supernatural, a mathematical artefact or pure form, therefore in Aristotle's
terminology they must be a kind of matter. The fields exist in various
states; these correspond to the different possible values of the
potential. Natural motion for electromagnetic fields can be towards
a flat potential or in the form of oscillating waves. Artificial motion
is movement from one field strength to another, induced by an external
source, a corpuscle.

So once again, we have a sequence. A particle induces motion (change of
state) in a field in its vicinity. The field at that location moves the
field at the point next to it to a different value, which again moves the
next bit of the field,
and so on until we reach the next particle. That particle is then moved
(accelerated) by the field, and in turn induces a further change of state
in the field. All of this happens 'simultaneously'. Although we have to
redefine a little what is meant by 'simultaneous. The motion propagates
along the field at the speed of light, and in that perspective it
might not seem to be simultaneous. However, the notion of time is
dependent on one's movement through space. The faster one moves, the slower
one's perception of time. If we are sitting on the wave
of motion in the electromagnetic field, it will seem as though time does
not pass; everything is instantaneous. So simultaneity depends on the
reference frame. But whether a series is hierarchical or accidental is
not frame dependent.

One of the determining factors of whether a series was hierarchical or
accidental was simultaneity of cause and effect. However, in special
relativity (and Maxwell's theory of electromagnetism is taking us to
special relativity), the concept of two events at different places being
at the same time is a difficult one to define. The naive interpretation,
inherited from Galileo (and Aristotle) posits an absolute time, which is
the same across all space. However, measurement of duration depends on
choice of coordinate system, and this is not absolute. Each observer
can choose their own system. Given that the speed of light is absolute
(the same in all inertial reference frames), observers travelling at
different speeds experience time differently. This contradicts the notion
of an absolute time; and without that, we lose the naive notion of things
being simultaneous at different locations. However, we can define simultaneous as meaning being
on the same light cone (this was Einstein's definition when
developing special relativity). That two things are on the same light cone
is not observer dependent. In this sense, we can say that the movement of
the field by the first particle is simultaneous with the movement of
the second particle by the field. The movement of the third particle by
the field will be simultaneous with the movement of the field by the
second particle. However, the interaction between the third particle
and the field need not be simultaneous with the interaction between the
first particle and the field. That concept is not intuitive, but when
you turn to non-Euclidean geometry you get a lot of concepts which are not
intuitive but happen to be right. We changed the definition of simultaneous;
some of the logic associated with the old way of thinking about it is no
longer valid. Thus we have local simultaneity between neighbours of the
chain, but
not global simultaneity between every member of the chain. But I would
say that that is enough to maintain the nature of a hierarchical series.

Equally, there is a direction in the sequence of causality. The corpuscle
moves the field which moves a corpuscle which moves the field which moves
a corpuscle and so on. This direction is not necessarily temporal;
that depends on the reference frame. But there is a definite sequence.
That sequence is not symmetrical. The way particles interact with fields
is different from the way that fields interact with particles. The series
is not static. There is motion.

So with regard to the criteria I listed above for identifying a
hierarchical, the first, fourth, and sixth conditions are
satisfied.

But now we come to the more difficult issues. Firstly, the series is not
as obviously
a linear chain of mover to moved. Particle A influences particle
B through the changes in the field along the line connecting them.
The field hits particle B, and then progresses out in every
direction, with the field strength getting a boost from particle B,
but still with indirect influence from A. That field then interacts
with particle C. So there is some indirect influence from
A to C, but also direct influence. It is sort of like a
stick with two prongs, pushing both the first stone and the second stone,
while the second stone is simultaneously pushed by both the first stone
and the stick. I don't think that this amendment is enough to affect
the underlying metaphysics. All the motion is directly or indirectly
dependent on the first member, so that's still consistent with the series
being hierarchical.

Then we have the worry that at the same time as A influences
B, B is influencing A. If it were truly the same time,
then that would put a huge dent in the idea that this is a hierarchical
sequence of movers and moved. It is no longer asymmetric.

However, although it is true that A's movement of the field can be
viewed as being simultaneous with B's movement by the field, and
that B's movement of the field is
viewed as being simultaneous with A's movement by the field, this
does not mean that A's movement of the field is simultaneous with
A movement by the field as induced by B in the same moment
that B is moved by the field coming from A. The two events
of A moving the field and its being moved are not on the same
light cone. The chain of interaction has to move from A to B
and then back again from B to A. There is a change of
direction in the middle there, which preserves the order of interaction.
It's non-Euclidean geometry playing havoc with our intuitive notions
again. And, of course, we now have the notion that two members of the
chain are the same being but at different moments in time. But that doesn't
stop the series being hierarchical; we would not complain if two of
Aristotle's stones were identical, and that's analogous to the situation
here. So the order of interaction is still
preserved, and we still maintain the asymmetry.

The next point of discussion is the requirement that the members of the
chain lack the
power to induce movement of themselves. It seems that this is violated in
the case of classical electromagnetism. Charged particles just have the
natural power to move electric fields. Or so it seems.

But this doesn't violate the principle that is needed for a hierarchical
series. The stick has the natural power to push a stone; but power isn't
activated unless the stick is put into a certain motion between various
states. Similarly, the power of the charged particle to move electric
fields does not mean that those fields will be moved. A static or
constant velocity particle generates a constant field (i.e. one unchanging
in time, in which
there is no motion). It is only when the particle accelerates that the
electric field is changed. A static field (this time meaning unchanging in
space) does not generate an electric force on a particle, but only one
which is different from one place to the next or changing in time.

Energy in physics is basically just a label of states. For each being,
there are numerous possible states it can be in. These states are
distinguishable, and so we need to attach a name to each state so we can
tell one from the other. Since we are trying to map these states to an
algebraic system, we use a set of numbers as the label. Those numbers are
known as the energy and momentum. Of course, there is no single unique
way of doing this. The choice that physicists use is advantageous because
total energy and momentum are conserved in every local interaction.
The principles of causality and special relativity guarantee that every
interaction is local, and this is true in practice for all the
interactions we know of.

In classical mechanics, the situation is complicated because the states
are also labelled by location. In quantum physics, this isn't the case.
Only energy, momentum, and a few other qualities (which don't really
influence this discussion) such as gauge,
polarisation and what physicists unfortunately call spin and colour
colour (nothing to do with the spin and colour we observe in the everyday
world) are required to label the states. But in either classical or
quantum physics, motion is movement from one energy state to another.
In classical physics, that is one of only two types of motion; in
quantum physics it is the only type of motion.

Each particle has a spectrum of possible energy states. In classical
physics, this spectrum is continuous; in quantum physics it is discrete
in certain bound systems such as the nucleon or the atom. This energy is
always positive (this is linked to the direction of time in quantum
physics), which means that the energy spectrum of a particle has a minimum
value. For a free massive particle, that minimum value is given by
E0 = mc2, where m is the particle's
mass and c is the speed of light, and I assume that we have chosen
our units so that there is no constant of proportionality (this equation
works if energy is measured in Joules, mass in kilograms, and the speed of
light in meters per second; it fails if energy is measured in calories,
mass in grams, and the speed of light in furlongs per Jovian year).
So you start with this value,
and build up from that a tower of possible energy states.

Note another interesting point of overlap with Aristotle's physics.
Aristotle stated that objects had a natural motion towards one particular
rest state, for the elements of earth and water the centre of the earth,
and could only be raised from that state by artificial motion. Well, he
got his theory of gravity and the elements wrong. But now we have another
tower of states, and one at the bottom, known as the ground state.
Particles have a natural motion towards the ground state, and will drop
there unless they are prevented from doing so (perhaps because it is
already occupied by other fermions). They can only rise up the tower
of states by artificial motion, an external interaction such as the
absorption of an incoming photon.

[Also, can we construct a first way argument defining motion as being
in a non-ground state. I don't think that this definition is true to
the spirit of Aristotle, but it certainly makes the everything can only
be raised from the ground state by something that isn't in the ground
state part of the argument clear. But we still need to show that it is
a hierarchical series.]

Now energy is always conserved. That means that if there is an interaction
between two particles (and here I include both corpuscles and fields),
then if the energy of the second of them increases, then
the energy of the first must decrease. But this is only possible if
the energy of the first particle had previously been raised above its
minimum value. So the first particle can only move the second if it had
previously been moved itself. In the case of electromagnetism, we can
start with two static particles and an electric field. The
electric field will be in a state of high energy, the particles (being
static in our laboratory frame) their minimum energy. Then energy is
gradually transferred from the electric field to the particles as they
approach each other.

That energy had to come to the electric field from somewhere (perhaps a
previous motion of the particles, as we put them into place), which had to
come from somewhere else, and so on. So just as the stone always has the
power to move another stone, but that power has to activated by the stone
itself being pushed (moved out of its minimum energy state), so the
electric field has the power to move the corpuscles, but needs that power
to be activated by it initially being moved into a higher energy state.

So it is not true that the particles solely act on their own power. They
act because they had previously been moved.

The only question which remains is that word previously? Does that
rule out the simultaneity needed in a hierarchical series? No. Firstly
because the starting position of this experiment is artificial. We are
holding the two corpuscles in place; applying a force to them. By doing
so, we set up another hierarchical series of movers and moved, only this
time involving ourselves. Secondly, previously here means
previously in the chain of causality rather than previously in time.

So we seem to have satisfied the conditions listed above for a
hierarchical series. However, this question is one which I would like to
see a professional philosopher give more attention to. I don't tend to see
it, either by detractors of the first way (who don't tend to understand
the argument well enough to get to this point), or
defenders of it (who don't tend to give a strong defence of this point
in terms of the actual interactions described by modern physics; mostly
they just use the basic contact pushing model of early classical physics
rather than the electromagnetic picture that classical physics adopted
when it reached its maturity).

Existential inertia

The objection.

Back to my internet adversary.

Existential inertia of material is manifest and evident to the senses.
Modern science calls this the conservation of mass/energy, described
with E=mc2. We never observe new mass/energy
persistently coming into existence, nor do we ever observe mass/energy
persistently ceasing to exist. The amount of mass/energy or material
remains constant, thus, material does not change in its existential
respect, only in its structure, or shape, or organization, or form.

Since the existential respect of material does not change no changer
is necessary. One can speculate that an unseen changer is actually
changing material in just the right way so that it appears to our
senses that no change in the existential respect of material is
occurring, but such a speculation is not necessary, and thus the Second
Way fails as an argument for the necessity of a hierarchical first
mover acting upon matter to sustain it in existence in the present
moment.

Response

Edward Feser again discussed existential inertia in his
Neo-Scholastic essays,
but this time I will go my own way. The questioner badly misunderstands
the physics (and advanced physics is one of Feser's weaknesses as well.
He needs to read my book). I will say it again: Energy is just a label
used to
distinguish different
stable or metastable states. Nothing more. Nothing less.
This definition can be used in
classical physics, but isn't usually, because classical physics is
usually taught without bringing in notions of states. And that's fine,
for the physicists. One can use the language of states to classical
physics, but it adds to the work that physicists have to do, without
really aiding the calculation. The point is that classical physics is
consistent with both the (stateless) mechanistic and the (requiring states)
Aristotelian philosophy. But it was developed by mechanists who were trying to find a way to
avoid Aristotle. So their notation and philosophy is usually used to teach it.
Of course, leaving states out had huge
philosophical consequences, but most classical physicists didn't care too
much about that because they didn't subscribe to Aristotelian philosophy.
So in the traditional way classical physics is taught (and the way it
historically developed), energy is just some mysterious number that
happens to be useful in the equations.

But when we come to quantum physics, particularly the more advanced
quantum field theory (QFT), the notion of states is unavoidable. The energy
operator (the Hamiltonian) is the time evolution operator. Thus stable
states are states of constant energy.

Now if energy is just a label, then it is not a thing. The things are the
particles themselves; the electrons, the photons, the quarks and so on.
When we discuss motion, we discuss one particular thing moving from one
energy state to another. The only requirement that we need when two or
more particles interact is that the sum of the numbers used to label the
energy of each particle remains constant.

Now, it can be that the energy of the initial particle is larger than
the minimum energy required to create new ones. For example, suppose we
have a photon which has the energy a little over twice the electron mass.
Among the rules we have to describe possible interactions are
conservation laws: of spin, energy/momentum,
electric charge and so on. The decay of the photon into an electron and
anti-electron is consistent with these rules. Thus it can happen. And it
does happen. All the time. In fact, every interaction in quantum field
theory -- thus every interaction in physics except (possibly) gravity --
is of this type. At least one particle is created or annihilated in each
interaction; the remaining particles (if not annihilated themselves)
move into a different state (i.e. have a different energy).

The objector is thus quite wrong. Firstly, he identifies mass (a
property essential to each type of particle, ultimately linked to
the strength of its interaction with the Higgs Boson) with energy
(a label describing
the accident of which particle state is actualised). Secondly, he states
that because energy is conserved, there is no change in the universe.
But change is precisely when energy is transferred from one particle
to another. That the total amount of energy is conserved is irrelevant.
Thirdly, he states that mass/energy doesn't change in its existential
aspect. But it does. An electron hurries along in a state with an energy
more than three times its rest mass. It emits a photon. The photon decays
into an electron/anti-electron pair. You started with one particle. You
now have three. New beings have come into existence.
If that's not a change in the existential aspect of the universe, I don't
know what is.

This notion of particles being emitted or absorbed is precisely what
Aristotle meant by efficient causality. Efficient causality (rather than
the alternative versions of causality introduced during the enlightenment
which focussed on events) links one particle, or more precisely one
particle state, with another. Take the example I gave in the previous
paragraph. The efficient cause of each of the the particles in the
electron/anti-electron pair is the photon. The efficient cause of the
photon is the initial electron. The efficient cause of the initial
electron in its final state is that electron in its initial state.
[A particle can, of course, have more than one efficient cause,
when defined in this way; or rather the efficient cause can be a set
of rather than a single particle].
Event causality is dead because of the spontaneous nature of particle
creation. But the notion of efficient causality, at least in this form,
is in a stronger evidential position now than it has ever been in human
history.

One of the problems that the person I am responding to had is that he
was still living in a mechanistic framework, where the fundamental
building blocks of matter could not be created or destroyed, only
rearranged. I don't think that his objection stands even in that
framework. Particles still move from one state to another. But his
knowledge of physics is a hundred years out of date. The mechanical
philosophy is dead,
buried, mourned for, had its obituary published in the Times, dug up by
archaeologists, and had its rotting remains displayed in the museum of
ancient artefacts as a prime example of philosophical dead ends.
Classical physics was its midwife; quantum physics its undertaker.

Objection

[This is one of mine.] But is the chain of efficient causes a hierarchical
rather than an accidental series? It seems that it is only an accidental
series, because the steps in the chain are not simultaneous with each
other.
It is not like the stick simultaneously moving the stone which
simultaneously
moves another stone which simultaneously moves another stone, and so on.
Instead, we have the electron gaining energy and then at a later time
emitting the photon, which then a little while later decays and so on.
There is a gap in time, so the series is more like a father begetting a
son, who begets another son, and so on, a series which is usually
described as being accidental.

Response

I raise this objection, because I would like to see a professional
philosopher address it. This is something of a weak point in my book
(one which I hope to address in a future revision). I say that the
series of efficient causes can't be infinite by falling
back to an argument from the second law of thermodynamics.
It has the weakness that it is an argument drawn
solely from physics (i.e. the natural), and there is a jump needed to get
to the supernatural. I use a variation of the Kalaam argument to get
to a supernatural cause, then jump back to Aquinas and his third way to
get from there to God. Now I think that this combination of arguments works, but I
still find it unsatisfying. The thing that stopped me from using the second
way (or argument from efficient causality) all the way to God was this
doubt that I could prove that the chain
of efficient causes is a hierarchical rather than an accidental series,
by using examples from QFT rather than the baby physics that Aristotelian
philosophers tend to illustrate their arguments with.

So if anyone has any ideas, I would be very grateful for the opportunity
to plagiarise them.

However, there is one thing I can say which is of importance.
In quantum physics, the energy and time operators don't commute.
That means that
time is undefined for a being in a definite energy state (possibly one
can connect this to the Aristotelian notion that time is a measure of
change, so something in a stable state doesn't change so doesn't have a
notion of time). The sequence I drew up of an electron emitting a photon
which in turn decays was expressed in the energy/momentum description of
reality. In that description, time is undefined. We can't say that
the interactions are instantaneous, simultaneous, or at different times
simply because there is no concept of time in the illustration
(at least for free, bare, unrenormalised particles -- which are rather
unphysical in themselves. For bound and complex states, it is a little
different).
To get back to a space/time formulation, we need to integrate over all
possible energy states (and thus in this case the energy of a particle is
undefined).
There is an order of causality,
but not an order in time. I don't know if this would help or hinder the
argument about whether this is a hierarchical or accidental series,
but it is something to bear in mind. [It's another place where
quantum physics defies any attempt we have to imagine or illustrate it
with macroscopic examples].

Indeed, since we are discussing special
relativity, we face the same problems in defining simultaneity as we did in
classical electromagnetism. We could fall back on the same definition
(two events on the same light cone are at the same time), and then we
could say that the creation of the electron/anti-electron pair is
simultaneous with the photon being emitted. But that doesn't address the
issue of the efficient cause of the original electron. Is that
in some sense inconsistent with it being an accidental series of causes
simultaneous with the photon decay later in the order of
causality? Does that matter?

Secondly, energy is still conserved. This is of the same importance as it
was in classical physics. Although every electron has the power to emit a
photon, that power can only be activated if it has enough energy. It had
to get that energy from something else, and that thing from something else,
and so on. So even though the emission of the photon is spontaneous, the
electron by itself cannot do so; it needs to have been moved into the
right state.

Note also the initial comment from the person I was replying to:

If an object needed a cause to persist in existence then a hierarchical
regress would be called for.

This statement, if it can be proved, might be a different way forward.
Obviously, it was originally stated as an argument against the hierarchical
regress; the claim was that things don't need a cause to persist. But
is that claim justified in the light of QFT?

One thing is clear: things don't naturally persist in existence.
That's the whole point
of QFT. There is a continual process of creation and annihilation going
on. That means that there is a genuine question of why things persist,
or at least seem
to persist. Indeed, the propagator of an object (which is the part of the
Hamiltonian which leads to the amplitude staying in the same state) is
made of an annihilation operator and a creation operator for the same state.
Whether that means that in reality the particle is going in and out of
existence, or that is just an artefact of the mathematical prescription is
harder to say. But there is nothing in the QFT toolbox which states that
things must persist. Spontaneous destruction is quite possible.
Now, physicists will shout at me here and say,
"What about physics? What about locality? The Hamiltonian contains both
the creation and annihilation operators, and there
are various good reasons why it would be inconsistent if it were otherwise."
I would
agree in everything said here except that it answers the question.
Physics just provides a description that things do seem to persist;
it doesn't provide an explanation of why; nor show that no explanation
is needed. We have to turn to the philosophy of physics. QFT shows us that
we can't just turn to some Newtonian concept of existential inertia,
because the annihilation operator exists, and represents a genuine physical
event.
But, in any
case, the idea of existential inertia is not something we should blindly
accept, because the process of spontaneous emission shows that things don't
have existential inertia. They don't naturally remain in the same state
if they are left alone.

So it seems likely to me that the same arguments that apply in classical
or Aristotelian
physics also apply here, and this series is a hierarchical series, but
I haven't yet been able to prove it to my satisfaction (let alone anyone
else's). Any suggestions would be welcome.

Objection

Does the conservation of energy preclude God's creation out of nothing.

Response

This is another objection I have put in, this time not because it is
something I doubt, but because this response is something I want to say.

For the theist, God is continually active upholding and sustaining the
universe (that's the difference between theism and deism). Physics
provides a mathematical description of how the universe is upheld and
sustained. It is relatively easy for the theist to connect the two
together. This, of course, is anathema to the atheist or the deist. They
regard as a first principle that the laws of physics operate independently
of God. But I have argued that it
is easier to deduce the the laws of physics from the theist perspective
than the atheist or deist ones. The symmetry requirements follow from
God's nature outside space and time, assuming that God is indifferent to
the universe. The indeterminacy of Quantum Physics
is a reflection of God's free will. The physical constants are constrained
by the
anthropic principle. Occasionalism is ruled out because God respects
the powers and natures of matter.

The principle of conservation of energy arises from the locality of the
theory, which in turn arises from the Lorentz symmetry of special
relativity combined with the principle of causality. The Lorentz symmetry
arises in part from the assumption that God is indifferent to the universe,
so there is no preferred inertial frame, so all observers in all inertial
frames experience God in the same way, so all observers in all inertial
frames experience the same physical Lagrangian. But, of course, most
religions and most especially Christianity deny that God is wholly
indifferent to the universe. God calls the Church to be a holy and
blameless people, and we can't achieve that without His help. Thus we
expect signs and events that provide evidence that the assumption of
God's indifference is at best only approximate (these events are
miracles). There is no reason in these cases for energy to be conserved,
since we have taken out one of the premises from which the conservation of
energy is deduced. Thus the philosophy on which both physics and theology
are built
is not inconsistent with miracles in
general, and the creation from nothing in particular. The law of efficient
causality is still maintained; only this time God would be the direct
efficient cause rather than an indirect one.

Remaining objections

The rest of the person I was asked to answer's objection was largely built
his initial misunderstanding of physics, so doesn't really go anywhere.
But there are a couple of points to make.

All these formulations suffer a major defect in that they posit
material changing itself at base in its existential respect. A-T
typically argues with naked eye examples, such as a cup of hot water,
which is observed to go from actually hot to potentially hot. This is a
change. To transition from actual to potential in a particular respect
is a change in that respect. In the case of the hot water that appears
to change itself but in truth the cup of hot water is not a single
material entity; rather it is composed of moving molecules. As those
molecules collide with the molecules of the air kinetic energy is
transferred in a vast number of mutually causal temporal interactions
with no change in the existential respect of the material of the
water-air system.

I actually agree with this point. I don't think that it helps the objection,
because as I have argued, once we get beyond the molecule "collisions"
(not that they really collide, but they transfer energy and momentum
through the exchange of photons), the microscopic interactions are not
inconsistent with the sequence of efficient causes. But I agree with him
that I wish that the philosophers would use examples from quantum field
theory. It is at the level of fundamental physics that it interacts with
philosophy, and the thermodynamics of coffee cups only indirectly.

When faced with a coffee cup or a banana, people's natural inclination is
to say "Well, yes, but mechanistic science has explained all that without
recourse to
all this nonsense about act and potentiality and final causes and so on."
And then they switch off,
and don't listen to anything else you, even if you are making a good and
sound point that goes beyond the illustration. You need to get to the
point where science demands that we introduce notions of potentiality and
finality, without any alternative mechanistic explanations. Of course,
that's a lot harder to explain. You need twelve chapters describing the
physics before you get to the good bit.

In the continual change speculation it may be asserted that material is
being continually changed, that is, moved from potentially existent to
actually existent. But non-existence has no potential to exist.
Non-existence has no potentialities at all.

But, just supposing non-existence could have the potential to exist how
would actually existent material be continually actualized to exist?
Actually existent material is already actualized in its existential
respect. A thing cannot be both potential and actual in the same
respect at the same time. So material would need to change itself to
not existing, so the unseen changer could change it back to existing,
or alternatively simply bring new material into being . Thus, a new
universe is continually being created, while the old universe is
continually being destroyed. This leads to severe problems with the
notion of temporal continuity of self, besides the rather fantastic
notion that the universe really was created a moment ago with the
appearance of age and all things in just the right state and just
the right motion so as to have the appearance of temporal continuity.

This looks closest of his arguments to the description we get in physics.
So I will address this one.

Firstly, his statement Non-existence has no potentialities at all.
That is just gibberish. Potentiality does not belong to concepts such as
existence or non-existence, but to form and substance. So we should say,
Can a non-existent being come into existence? Or rather, (since
this obviously happens) can the framework of potentiality and actuality
cope with this situation? Yes it can. The final causes of an electron
include the creation of a photon. The notion of actuality and potentiality
is invoked to describe the notion of change of state in a being that
continues to exist. But there is no difficultly in tacking on the idea that
as well as beings moving from one state to another, there is also creation
of new particles.

Are these called out of non-existence? No. Because non-existence isn't a
thing. They have the efficient cause of the particle that emitted them.
It is not a case of continual creation and destruction of the universe.
Firstly, each interaction is local. It doesn't involve the whole universe,
but only the particles affected. Secondly, energy eigenstates aren't
temporal eigenstates. You don't have destruction then re-creation in the
next moment of time. (You might have destruction and then re-creation,
or might not,
but it isn't in time.) Discussion of moments of time doesn't make sense in
this context. Thirdly, particles of the same type are identical. One
can't tell if the electron at the start of an experiment is the same one
as the electron at the end of the experiment. An electron could continue
as it were, or it could emit a photon, which decays into an
electron/anti-electron pair, where the anti-electron annihilates with the
original electron into a photon which is absorbed into the second electron.
We are left with an electron of the same energy and momentum, but it's not
the same one we started with. But why does that matter? It is identical to
it in every respect, and there is still the sense of continuity contained
within the sequence of efficient causes. The original state is still the
efficient cause of the final state in either case, and this allows us to
maintain a temporal continuity of ourselves.

Thus, the Second Way, the argument from efficient cause, fails as an
argument for the necessity of a hierarchical first changer in the
present moment to account for the observation of existential inertia
that is manifest and evident to our senses.

No the second way doesn't fail (at least, not for this reason).
Because there is no such thing as existential inertia.

Dear Dr. Cundy, first, I love your blog - mostly for its integrated thought and internal honesty as you admit to trying to sort it all out along with everyone else.

I have one semester of physics for non-majors under my belt, I play at philosophy, and I have a Masters in Theological Studies, so basically, regarding this area, I don't much know what I am talking about - and yet, here goes.

I am wondering if it affects/aids your arguments if we recall that while the term used by Aristotle is movement, and most of the descriptions given involve some kind of movement in space and time, what he was actually talking about was movement from potential to actual? This is usually couched as "change" these days, but it is type of movement from one state to another. I wonder because of these quotes from your post:

"I will say it again: Energy is just a label used to distinguish different stable or metastable states. Nothing more. Nothing less"

And:

"Now if energy is just a label, then it is not a thing. The things are the particles themselves; the electrons, the photons, the quarks and so on. When we discuss motion, we discuss one particular thing moving from one energy state to another."

From one energy state to another - from potential to actual?

And next I go way outside my knowledge base with a thought regarding time, and a persistent nagging thought that it may somehow apply, though I honestly cannot see just how - I wonder if time is simply the expansion of the universe. Is the arrow of time simply that expansion? And is this expansion simply the continuing movement from potential to actual? The song of God continuously creating the Universe? (To borrow from Tolkien.)

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